MATHEMATICS –II
COURSE OBJECTIVES
This course is designed to give a comprehensive coverage at an introductory level to the subject of matrices, integral calculus, coordinate geometry, basic elements of vector algebra and first order differential equations.
COURSE OUTCOMES
After undergoing this course, the students will be able to:
- Solve linear equations using determinants and matrix algebra.
- Perform integration techniques, solve area and volume problems.
- Solve first order differential equations and apply numerical methods.
- Form and interpret equations of lines, circles and conics.
- Perform vector operations and solve related engineering problems of relevant branch.
COURSE CONTENTS
UNIT – I: Determinants and Matrices
Elementary properties of determinants up to 3rd order, consistency of equations, Crammer’s rule. Algebra of matrices, inverse of a matrix, matrix inverse method to solve a system of linear equations in three variables.
UNIT – II: Integral Calculus
Integration as inverse operation of differentiation. Simple integration by substitution, by parts and by partial fractions (for linear factors only). Introduction to definite integration. Use of formulae 𝜋∫02sin𝑛𝑥𝑑𝑥,𝜋∫02cos𝑛𝑥𝑑𝑥,𝜋∫02sin𝑚𝑥cos𝑛𝑥𝑑𝑥 for solving problems ,where m and n are positive integers.
Applications of integration for (i). Simple problems on evaluation of area bounded by a curve and axes.
(ii). calculation of volume of a solid formed by revolution of an area about axes. (Simple problems).
UNIT-III: Differential Equations & Numerical Methods (15 periods)
Definition of differential Equations, order and degree of a differential equation, formation of differential equations, solution of first order and first degree differential equations by variable separable method (simple problems). Trapezoidal rule, Simpson’s 1/3 and Simpson’s 3/8 rule and their applications in simple cases. MATLAB – Simple Introduction.
UNIT – IV: Two dimensional Co-Ordinate Geometry
Equation of straight line in various standard forms (without proof), intersection of two straightlines, angle between two lines. Parallel and perpendicular lines, perpendicular distance formula.
General equation of a circle and its characteristics. To find the equation of a circle, given:
i. Centre and radius,
ii. Three points lying on it and
iii. Co-ordinates of end points of a diameter;
Definition of conics(Parabola, Ellipse, Hyperbola), their standard equations without proof. Problems on conics when their foci, directories or vertices are given.
UNIT – V: Vector Algebra
Definition notation and rectangular resolution of a vector. Addition and subtraction of vectors. Scalar and vector product of two vectors. Simple problems related to work, moment and angular velocity.
INSTRUCTIONAL STRATEGY
The content of this course is to be taught on conceptual basis with plenty of real world examples. Differential equations and applications of differential equations can be taught with engineering applications of relevant branch.
MEANS OF ASSESSMENT
- Assignments and Quiz/Class Tests
- Mid-term and End-term Written Tests
- Model/Prototype Making
RECOMMENDED BOOKS
- B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, New Delhi, 40th Edition, 2007.
- G. B. Thomas, R. L. Finney, Calculus and Analytic Geometry, Addison Wesley, 9th Edition, 1995.
- S.S. Sabharwal, Sunita Jain, Eagle Parkashan, Applied Mathematics, Vol. I & II, Jalandhar.
- Comprehensive Mathematics, Vol. I & II by Laxmi Publications, Delhi.
- Reena Garg & Chandrika Prasad, Advanced Engineering Mathematics, Khanna Publishing House, New Delhi